cube files
Indexed Cube Lovers Archive
God's Algorithm to 13q, Summarized by Symmetry Class
Submitted by Jerry Bryan on Mon, 02/26/2007 - 12:25.
God's Algorithm to 13q has been posted before, but it has not been summarized by symmetry class. The symmetry classes in the table below follow Dan Hoey's taxonomy.
|x| Symmetry Size Patterns Positions
Class of
xM
0 M 1 1 1
Total 1 1
1 CR 12 1 12
Total 1 12
2 I 48 2 96
Q 6 1 6
R 6 1 6
CX 6 1 6
Total 5 114
3 I 48 20 960
ES 24 4 96
CR 12 1 12
Total 25 1068
4 I 48 200 9600
HV 24 1 24
HW 24 3 72
ES 24 12 288
EX 12 2 24
X 3 1 3
Total 219 10011
5 I 48 1932 92736
ES 24 46 1104
Total 1978 93840
6 I 48 18232 875136
HV 24 4 96
AV 24 1 24
HW 24 12 288
ES 24 132 3168
HS 12 2 24
HQ 12 2 24
EX 12 10 120
Total 18395 878880
7 I 48 171039 8209872
CV 24 8 192
ES 24 482 11568
Total 171529 8221632
8 I 48 1600143 76806864
HV 24 27 648
AV 24 11 264
CV 24 30 720
HW 24 72 1728
ES 24 1345 32280
V 12 4 48
W 12 2 24
HS 12 10 120
HQ 12 6 72
AP 12 17 204
CS 12 10 120
EX 12 36 432
HT 8 1 8
P 6 4 24
HX 6 6 36
X 3 1 3
Total 1601725 76843595
9 I 48 14951634 717678432
HV 24 8 192
AV 24 4 96
CV 24 78 1872
HW 24 4 96
ES 24 4536 108864
CR 12 2 24
Total 14956266 717789576
10 I 48 139614140 6701478720
HV 24 304 7296
AV 24 36 864
CV 24 188 4512
HW 24 479 11496
ES 24 13792 331008
ET 16 1 16
V 12 3 36
W 12 5 60
HS 12 22 264
CR 12 6 72
HQ 12 23 276
AP 12 13 156
CS 12 27 324
EX 12 138 1656
S 6 1 6
Q 6 2 12
R 6 3 18
P 6 6 36
AX 6 1 6
CX 6 4 24
Total 139629194 6701836858
11 I 48 1303095550 62548586400
HV 24 92 2208
AV 24 18 432
CV 24 640 15360
HW 24 126 3024
ES 24 41965 1007160
ET 16 4 64
CR 12 40 480
AP 12 10 120
Total 1303138445 62549615248
12 I 48 12157642376 583566834048
HV 24 3051 73224
AV 24 320 7680
CV 24 1814 43536
HW 24 3790 90960
ES 24 126636 3039264
ET 16 9 144
V 12 38 456
W 12 25 300
HS 12 135 1620
AS 12 8 96
CR 12 85 1020
HQ 12 105 1260
AP 12 80 960
CS 12 111 1332
EX 12 372 4464
HT 8 1 8
CT 8 2 16
S 6 9 54
Q 6 11 66
R 6 1 6
P 6 25 150
HX 6 27 162
AX 6 6 36
CX 6 15 90
E 4 2 8
X 3 12 36
M 1 1 1
Total 12157779067 583570100997
13 I 48 113382128780 5442342181440
HV 24 1431 34344
AV 24 264 6336
CV 24 7387 177288
HW 24 2046 49104
ES 24 382235 9173640
ET 16 2 32
CR 12 205 2460
AP 12 32 384
Total 113382522382 5442351625028
